Does Google have a free QR code generator?

Yes — Google Chrome has a built-in free QR code generator: on any web page, open the share menu (or the three-dot menu) and choose 'Create QR code'. Google Sheets and Slides can also generate codes via formulas or add-ons. All of these produce static codes.

The limitations: Chrome's codes only encode the page URL (no WiFi, vCard or text types), there are no design options beyond a basic style, and — because they're static — you can't change the destination later or see scan counts. That's fine for sharing a link quickly. For printed material, a proper generator gives you logo and color options, correct sizing for print, and the choice of dynamic codes when you need editing or analytics.